Question

If the equation given by $ hxy + 10x +6y +4 = 0 $ represents a pair of lines, then $ h $ is equal to

• A. $ 15 $
• B. $ 30 $
• C. $ 5 $
• D. $ 10 $

Answer 1

Answer: (A)

Here, $a=0,\,\, b=0,\,\, h=\frac{h}{2}, \,\,g=5, \,\,f=3$ and $c=4$
It represent a pair of lines
$\therefore \begin{vmatrix}0&h /2&5\\ h /2&0&3\\ 5&3&4\end{vmatrix}=0$
$\Rightarrow 0-\frac{h}{2}\left[4 \frac{h}{2}-15\right]+5\left[\frac{3 h}{2}-0\right]=0$
$\Rightarrow \,\,\,-h^{2}+\frac{h 15}{2}+\frac{15 h}{2}=0$
$\Rightarrow \,\,\,-h^{2}+15 h=0$
$\Rightarrow \,\,\,h(-h+15)=0$
$\Rightarrow \,\,\,h=0,15$